Black Shop Ind wrote: I tried making photos on an external drive visible to Photos. Photos appears to have made a copy of itself on the external drive.
I don't understand this. The Photos app uses data in a Photos Library with the extension of ".photoslibrary" Are you saying that you created a Photos Library on an external drive? It is true that, if the Photos app does not see a Photos Library to use, it will create an empty one. Photos can't open without a Library.
You don't tell us the format of your external drive. To avoid damaging the Photos Library an external drive must be formatted in either APFS format or Mac OS Extended (Journaled) format. There have been so many problems with using incompatible drives that the newest macOSs won't even allow a Library on a non-Mac formatted drive to open, since there is a chance of damaging the Photos database. See this:
Move your Photos library to save space on your Mac - Apple Support
A Mac can have more than one Photos Library, but only the System Library can connect to iCloud. Is your active Library the System Library? You can find out with Photos' Settings>General:

This shows the path to the Library and a button to push if this is not the System Library. Here the button is grayed out because this is already the System Library. Be sure that "Copy" is checked.
Pictures can be imported to a Photos Library with the menu choice File>Import. You connect this System Library to iCloud with Photos' Settings>iCloud

Let us know how it goes…